The youngsters died from gas poisoning after the blaze broke out at the Winter Cherry shopping centre, according to reports.
At least 60 firefighters were scrambled to the scene at around 4pm local time (10am UK time) as panicked shoppers fled from the mall.
Shocking footage has emerged of emerged of people jumping from windows in a desperate attempt to escape the inferno.
A source told state news site Sputink: "According to the preliminary data, four children have died as result of gas poisoning after the fire."
Rescuers are still at the scene, attempting to free those trapped inside the shopping centre.
A spokesman for Russia's Ministry of Emergency Situations said: "100 people were evacuated and 20 people were rescued."
News agency Tass quoted the city's mayor saying that at least 10 people, including two children, have been rushed to hospital.
The case of the fire is as yet unknown and the victims have not been identified.
However, the blaze is thought to started on the fourth floor, where a cinema and a children's entertainment centre are located.
Russia's Investigative Committee this afternoon announced it had launched a criminal investigation into the case.
The traffic in the area around the shopping mall, which is close to Kemerovo's main train station, has been blocked.
Kemerovo is more than 1850 miles from Moscow, the Russian capital.